They say that all roads lead to calculus. As a quintessential aspect in advanced studies of the natural sciences and other math-related fields, TOPS introduces calculus to its students in grade 11—a full year before it is presented in the standard curriculum. This course is studied as the MHF4U (Advanced Functions) credit.
Students may choose between the AP Calculus AB course or the AP Calculus BC course, which provides a more in-depth examination of the subject. Within half the semester, students complete the Ontario curriculum content which emphasizes derivatives and their application. Students at TOPS spend their remaining time building upon this knowledge to work on integration, dealing in topics such as the volumes of revolutions. This makes the course much more comparable to an AP Calculus level course. Finally, to completely cover the AP curriculum, which cannot usually be done in half a year, students may attend optional classes after school to study parametric equations, differentials, and convergence tests, amongst other topics.
Many students go on to take the AP Calculus exam following this course, and several perform very well on the exam. Students finish the course with a thorough understanding of Calculus–in fact, many TOPS graduates have come back to say that this enriched learning has made their first, second, or even third years of university calculus easier.